Apparatus and method for detecting signal by maximum likelihood

ABSTRACT

An apparatus and method for detecting a signal in a receiver by maximum likelihood (ML) are provided, in which symbols are detected according to the number of transmit antennas of a transmitter and a modulation scheme, channels are estimated, an equivalent channel matrix corresponding to the estimated channels is determined, a permuted equivalent channel matrix is determined by multiplying the equivalent channel matrix by a predetermined permutation matrix, the permuted equivalent channel matrix is QR decomposed, a hard decision is performed on predetermined symbols among the detected symbols using a received signal resulting from the QR decomposition, and the log likelihood ratios (LLRs) of the hard-decided symbols are determined.

CROSS-REFERENCE TO RELATED APPLICATION(S) AND CLAIM OF PRIORITY

The present application claims the benefit under 35 U.S.C. §119(a) of aKorean Patent Application filed in the Korean Intellectual PropertyOffice on Jun. 12, 2007 and assigned Serial No. 2007-57243, the entiredisclosure of which is hereby incorporated by reference.

TECHNICAL FIELD OF THE INVENTION

The present invention generally relates to a wireless communicationsystem. More particularly, the present invention relates to an apparatusand method for detecting a signal by maximum likelihood (ML).

BACKGROUND OF THE INVENTION

In general, a wireless communication system with multipletransmit/receive antennas has a larger channel capacity than asingle-antenna wireless communication system.

Double space time transmit diversity (DSTTD) implements two AlamoutiSTTDs. The Alamouti STTD-based communication system achieves a transmitdiversity gain, especially a spatial multiplexing gain, due to itsparallel structure. Meanwhile, the multi-antenna wireless communicationsystem can operate using orthogonal frequency division multiplexing(OFDM) to minimize frequency selective fading.

To obtain optimal performance, a DSTTD-OFDM communication system shoulduse an ML receiver. However, real implementation of the DSTTD-OFDMcommunication system is hard because the use of an ML receiver requiresexponential functional complexity in the number of transmit antennas andthe modulation order used.

SUMMARY OF THE INVENTION

To address the above-discussed deficiencies of the prior art, it is aprimary aspect of exemplary embodiments of the present invention toaddress at least the problems and/or disadvantages and to provide atleast the advantages described below. Accordingly, an aspect ofexemplary embodiments of the present invention is to provide an MLdetection apparatus and method for reducing computational volume.

In accordance with an aspect of exemplary embodiments of the presentinvention, there is provided a method for detecting symbols from areceived signal according to the number of transmit antennas of atransmitter and a modulation scheme; estimating channels using thedetected symbols; determining an equivalent channel matrix correspondingto the estimated channels; determining a permuted equivalent channelmatrix by multiplying the equivalent channel matrix by a predeterminedpermutation matrix; performing QR decomposition on the permutedequivalent channel matrix; performing a hard decision on first symbolsamong the detected symbols using symbols obtained from the QRdecomposition; and determining the log likelihood ratios (LLRs) ofsecond symbols other than the first symbol among the detected symbolsusing the hard-decided symbols and combinations of the first symbols.

In accordance with another aspect of exemplary embodiments of thepresent invention, there is provided an apparatus for detecting a signalin a receiver by ML, in which a symbol detector for detecting symbolsfrom a received signal according to the number of transmit antennas of atransmitter and a modulation scheme; a channel estimator for estimatingchannels and determining an equivalent channel matrix corresponding tothe estimated channels; a QR decomposer for determining a permutedequivalent channel matrix by multiplying the equivalent channel matrixby a predetermined permutation matrix and performing QR decomposition onthe permuted equivalent channel matrix; and a log likelihood ratios(LLR) calculator for performing hard decision on first symbols among thedetected symbols using the symbols obtained from the QR decompositionand determining the log likelihood ratios (LLRs) of second symbols otherthan the first symbol among the detected symbols using the hard-decidedsymbols and combinations of the first symbols.

Before undertaking the DETAILED DESCRIPTION OF THE INVENTION below, itmay be advantageous to set forth definitions of certain words andphrases used throughout this patent document: the terms “include” and“comprise,” as well as derivatives thereof, mean inclusion withoutlimitation; the term “or,” is inclusive, meaning and/or; the phrases“associated with” and “associated therewith,” as well as derivativesthereof, may mean to include, be included within, interconnect with,contain, be contained within, connect to or with, couple to or with, becommunicable with, cooperate with, interleave, juxtapose, be proximateto, be bound to or with, have, have a property of, or the like.Definitions for certain words and phrases are provided throughout thispatent document, those of ordinary skill in the art should understandthat in many, if not most instances, such definitions apply to prior, aswell as future uses of such defined words and phrases.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of the present disclosure and itsadvantages, reference is now made to the following description taken inconjunction with the accompanying drawings, in which like referencenumerals represent like parts:

FIG. 1 is a block diagram of a receiver in a DSTTD-OFDM communicationsystem to which the present invention can be applied;

FIGS. 2 and 3 are detailed block diagrams of ML detectors according toexemplary embodiments of the present invention;

FIG. 4 is a flowchart illustrating an ML detection operation in thereceiver according to an exemplary embodiment of the present invention;and

FIG. 5 is a graph comparing ML detection schemes according to exemplaryembodiments of the present invention with a conventional ML detectionscheme in terms of computational volume.

Throughout the drawings, the same drawing reference numerals will beunderstood to refer to the same elements, features and structures.

DETAILED DESCRIPTION OF THE INVENTION

FIGS. 1 through 5, discussed below, and the various embodiments used todescribe the principles of the present disclosure in this patentdocument are by way of illustration only and should not be construed inany way to limit the scope of the disclosure. Those skilled in the artwill understand that the principles of the present disclosure may beimplemented in any suitably arranged wireless communication system.

Exemplary embodiments of the present invention provide an ML detectionapparatus and method for reducing computational volume in amulti-antenna wireless communication system. This wireless communicationsystem can be a DSTTD-OFDM communication system.

FIG. 1 is a block diagram of a receiver in a DSTTD-OFDM communicationsystem to which the present invention can be applied.

Referring to FIG. 1, the receiver includes OFDM demodulators 102 and 104for demodulating received OFDM signals, a symbol detector 106 fordetecting symbols received during a predetermined number of symbolintervals from the demodulated OFDM signals, an ML detector 108 forML-detecting the detected symbols, a parallel-to-serial (P/S) converter110 for converting parallel signals to a serial signal, a deinterleaver112 for deinterleaving the serial signal, and a decoder 114 for decodingthe deinterleaved signal. The ML detector 108 performs ML detectionschemes for reducing computational volume according to the presentinvention.

A description will be made of a first ML detection scheme for reducingcomputational volume, and a second ML detection scheme being animprovement of the first ML detection scheme in the DSTTD-OFDMcommunication system according to exemplary embodiments of the presentinvention.

Compared to a conventional ML detection scheme that requirescomputations for a total of lΩl⁴ candidates to decide the log likelihoodratios (LLRs) of a symbol to be decoded, the first ML detection schemeof the present invention needs computations for no more than 2lΩl²candidates and the second ML detection scheme advanced from the first MLdetection scheme needs only 2lΩl² candidates to determine the LLR. Ωrepresents a set of all candidates for a single transmitted symbol, andlΩl represents the number of elements in the set.

1. First ML Detection Scheme

Before describing the first ML detection scheme, it is assumed thatDSTTD-OFDM channels experience frequency selective fading, the cyclicprefix (CP) length is longer than the channel impulse response, and thechannel response is frequency-flat, constant for one frame duration.

A coding matrix for subcarrier k is:

$\begin{matrix}{{C^{k} = \begin{bmatrix}s_{1}^{k} & s_{2}^{k} & s_{3}^{k} & s_{4}^{k} \\{- s_{2}^{k*}} & s_{1}^{k*} & {- s_{4}^{k*}} & s_{3}^{k*}\end{bmatrix}^{T}},} & \left\lbrack {{Eqn}.\mspace{14mu} 1} \right\rbrack\end{matrix}$

and a vector received on subcarrier k is:

$\begin{matrix}{{r^{k} = {{H^{k}C^{k}} + {\underset{\_}{n}}^{k}}}{H^{k} = {\begin{bmatrix}h_{11}^{k} & h_{12}^{k} & h_{13}^{k} & h_{14}^{k} \\h_{21}^{k} & h_{22}^{k} & h_{23}^{k} & h_{24}^{k}\end{bmatrix}.}}} & \left\lbrack {{Eqn}.\mspace{14mu} 2} \right\rbrack\end{matrix}$

For signals received during two symbol intervals at the receiver afterCP elimination, the equivalent signal model is given as:

$\begin{matrix}{{H^{k} = \begin{bmatrix}h_{11}^{k} & h_{12}^{k} & h_{13}^{k} & h_{14}^{k} \\h_{21}^{k} & h_{22}^{k} & h_{23}^{k} & h_{24}^{k}\end{bmatrix}}{y^{k} = \left\lbrack {{r_{1}^{k}\left( {2n} \right)}{r_{1}^{k*}\left( {{2n} + 1} \right)}{r_{2}^{k}\left( {2n} \right)}{r_{2}^{k*}\left( {{2n} + 1} \right)}} \right\rbrack^{T}}{y^{k} = {{H_{eff}^{k}s^{k}} + n^{k}}}{{H_{eff}^{k} = \begin{bmatrix}h_{11}^{k} & h_{12}^{k} & h_{13}^{k} & h_{14}^{k} \\h_{12}^{k*} & {- h_{11}^{k*}} & h_{14}^{k*} & {- h_{13}^{k*}} \\h_{21}^{k} & h_{22}^{k} & h_{23}^{k} & h_{24}^{k} \\h_{22}^{k*} & {- h_{21}^{k*}} & h_{24}^{k*} & {- h_{23}^{k*}}\end{bmatrix}},}} & \left\lbrack {{Eqn}.\mspace{14mu} 3} \right\rbrack\end{matrix}$

where s^(k) denotes a symbol vector transmitted on subcarrier kexpressed as s^(k)=[s₁ ^(k) s₂ ^(k) s₃ ^(k) s₄ ^(k)]^(T), h_(ij) ^(k)denotes a channel frequency response that subcarrier k experiencesbetween a j^(th) transmit antenna and an i^(th) receive antennaexpressed as

$h_{ij}^{k} = {\sum\limits_{l = 1}^{L}{{h_{ij}(l)}^{{- j}\frac{2\pi \; {kl}}{N_{c}}}}}$

where N_(c) is a fast Fourier transform (FFT) size and L is the lengthof a channel impulse response, n denotes the index of an OFDM symbol,and H_(eff) ^(k) denotes an equivalent channel matrix representing thecharacteristics of channels.

If the equivalent channel matrix H_(eff) ^(k) is to be QR-decomposed,permutation should precede the QR decomposition. The equivalent channelmatrix is first permuted using a predetermined permutation matrix andthen QR-decomposed. QR decomposition is decomposition of a given matrixinto a unitary matrix Q and an upper triangular matrix R.

Hereinafter, H_(eff) ^(k) will be described separately as H_(eff) ^(U)and H_(eff) ^(D). Hence, H_(eff) ^((U))=π^((U))H_(eff) and H_(eff)^((U))=Q^((U))R^((U)) where Q is a unitary matrix, R is an uppertriangular matrix, and π^((U)) is the predetermined permutation matrix.The permutation matrix π^((U)) can be:

$\begin{matrix}{{\Pi^{(U)} = \begin{bmatrix}1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & 1 & 0 \\0 & 0 & 0 & 1\end{bmatrix}},} & \left\lbrack {{Eqn}.\mspace{14mu} 4} \right\rbrack\end{matrix}$

and the upper triangular matrix R^((U)) is given as:

$\begin{matrix}{= {\begin{bmatrix}R_{1,1}^{(U)} & 0 & R_{1,3}^{(U)} & R_{1,4}^{(U)} \\0 & R_{1,1}^{(U)} & {- R_{1,4}^{{(U)}*}} & R_{1,3}^{{(U)}*} \\0 & 0 & R_{3,3}^{(U)} & 0 \\0 & 0 & 0 & R_{3,3}^{(U)}\end{bmatrix}.}} & \left\lbrack {{Eqn}.\mspace{14mu} 5} \right\rbrack\end{matrix}$

Using Equation 4 and Equation 5, the LLRs of a transmitted symbol can becomputed by:

$\begin{matrix}{{{\overset{\sim}{y} = {{Q^{{(U)}H}y} = {{R^{(U)}s} + {\overset{\sim}{n}}^{(U)}}}},{{\Pr \left( {\overset{\sim}{y}s} \right)} = {\frac{1}{\left( {2{\pi\sigma}^{2}} \right)^{N_{r}}}{\exp\left( {{- \frac{1}{2\sigma^{2}}}{{\overset{\sim}{y} - {R^{(U)}s}}}^{2}} \right)}}}}{{L\; L\; {R\left( b_{i}^{q} \right)}} \approx {\frac{1}{2\sigma^{2}}\begin{pmatrix}{{\min\limits_{{s_{k}b_{i}^{q}} = {- 1}}{{\overset{\sim}{y} - {R^{(U)}s_{k}}}}^{2}} -} \\{\min\limits_{{s_{k}b_{i}^{q}} = {+ 1}}{{\overset{\sim}{y} - {R^{(U)}s_{k}}}}^{2}}\end{pmatrix}}}{q\text{:}\mspace{14mu} {the}\mspace{14mu} q\text{-}{th}\mspace{14mu} {transmitter}},{i\text{:}\mspace{14mu} {the}\mspace{14mu} i\text{-}{th}\mspace{14mu} {bit}},} & \left\lbrack {{Eqn}.\mspace{14mu} 6} \right\rbrack\end{matrix}$

where Pr({tilde over (y)}|s) denotes the probability of receiving asignal y when the transmitted symbol vector is s, σ² denotes a noisepower, b_(i) ^(q) denotes an i^(th) bit of a q^(th) transmitted symbol,and s_(k) denotes a k^(th) transmitted symbol vector among all possibletransmitted symbol vectors.

After the QR decomposition, the received signal vector can be expressedas:

{tilde over (y)}=Q ^((U)H) y=R ^((U)) s+ñ ^((U)),

{tilde over (y)} ₁ ^((U)) =R ₁₁ ^((U)) s ₁ +R ₁₃ ^((U)) s ₃ +R ₁₄ ^((U))s ₄ +ñ ₁ ^((U))

{tilde over (y)} ₂ ^((U)) =R ₁₁ ^((U)) s ₂ +R ₁₄ ^(*(U)) s ₃ −R ₁₃^(*(U)) s ₄ +ñ ₂ ^((U)).

{tilde over (y)} ₃ ^((U)) =R ₃₃ ^((U)) s ₃ +ñ ₃ ^((U))

{tilde over (y)} ₄ ^((U)) =R ₃₃ ^((U)) s ₄ +ñ ₄ ^((U))  [Eqn. 7]

{tilde over (y)}₁ ^((U)) and {tilde over (y)}₂ ^((U)) depicted inEquation 7 will first be described below.

If the ML result of [s₃, s₄]^(T) is already known, [s₁, s₂]^(T) can befound out by Decision-Feedback (DF) detection with hard decision withoutcalculating Euclidean distances. However, to find out the ML result of[s₃, s₄]^(T), all possible combinations of [s₃, s₄]^(T) should beconsidered. While all possible [s₁, s₂]^(T) values can be obtained byapplying the DF detection with hard decision scheme to each [s₃, s₄]^(T)combination, all possible combinations of [s₃, s₄]^(T) should be takeninto account to obtain the ML result of [s₃, s₄]^(T).

Each of the number of total candidates of [s₁, s₂]^(T) including the MLresult of [s₁, s₂]^(T) and the number of total candidates of [s₃,s₄]^(T) including the ML result of [s₃, s₄]^(T) is lΩl². Meanwhile,since all possible candidates are considered for [s₃, s₄]^(T), accurateLLRs of [s₃, s₄]^(T) can be detected, but it may occur that the LLR of aparticular bit in [s₁, s₂]^(T) cannot be calculated. Therefore, the LLRsof [s₃, s₄]^(T) are determined by:

$\begin{matrix}{{\Phi^{(U)}\text{:}\mspace{14mu} {candidate}\mspace{14mu} {vector}\mspace{14mu} {from}\mspace{14mu} {all}\mspace{14mu} {possible}\mspace{14mu} {combinations}\mspace{14mu} {of}\mspace{14mu} s_{3}\mspace{14mu} {and}\mspace{14mu} s_{4}\mspace{14mu} {with}\mspace{14mu} D\; F\mspace{14mu} {detection}}\mspace{79mu} {{{\Phi^{(U)}}\text{:}\mspace{14mu} {the}\mspace{14mu} {cardinality}\mspace{14mu} {of}\mspace{14mu} \Phi^{(U)}},{{i.e.\mspace{11mu} {\Phi^{(U)}}} = {\Omega }^{2}}}\mspace{79mu} {s_{k}\text{:}\mspace{14mu} {element}\mspace{14mu} {of}\mspace{14mu} \Phi^{(U)}}\mspace{79mu} {{{L\; L\; {R\left( b_{i}^{q} \right)}} \approx {\frac{1}{2\sigma^{2}}\begin{pmatrix}{{\min\limits_{{{s_{k} \in \Phi^{(U)}}b_{i}^{q}} = {- 1}}{{\overset{\sim}{y} - {R^{(U)}s_{k}}}}^{2}} -} \\{\min\limits_{{{s_{k} \in \Phi^{(U)}}b_{i}^{q}} = {+ 1}}{{\overset{\sim}{y} - {R^{(U)}s_{k}}}}^{2}}\end{pmatrix}}},\mspace{79mu} {q \in {\left\{ {3,4} \right\}.}}}} & \left\lbrack {{Eqn}.\mspace{14mu} 8} \right\rbrack\end{matrix}$

Now how the LLRs of [s₁, s₂]^(T) are decided will be described.

The following permuted equivalent channel matrix H_(eff) ^((D)) isconsidered:

$\begin{matrix}{{H_{eff}^{(D)} = {\Pi^{(D)}H_{eff}}},{\Pi^{(D)} = {\begin{bmatrix}0 & 0 & 1 & 0 \\0 & 0 & 0 & 1 \\1 & 0 & 0 & 0 \\0 & 1 & 0 & 0\end{bmatrix}.}}} & \left\lbrack {{Eqn}.\mspace{14mu} 9} \right\rbrack\end{matrix}$

As in Equation 5, H_(eff) ^((D)) is QR-decomposed into:

$\begin{matrix}{{H_{eff}^{(D)} - {Q^{(D)}R^{(D)}}}{R^{(D)} = {\begin{bmatrix}R_{1,1}^{(D)} & 0 & R_{1,3}^{(D)} & R_{1,4}^{(D)} \\0 & R_{1,1}^{(D)} & {- R_{1,4}^{{(D)}*}} & R_{1,3}^{{(D)}*} \\0 & 0 & R_{3,3}^{(D)} & 0 \\0 & 0 & 0 & R_{3,3}^{(D)}\end{bmatrix}.}}} & \left\lbrack {{Eqn}.\mspace{14mu} 10} \right\rbrack\end{matrix}$

The permutation matrix π^((D)) permutes the sequence of the transmittedsignal vector according to Equation 11, and the resulting changedreceived signal vector is given by Equation 12:

{tilde over (s)}=[s ₃ s ₄ s ₁ s ₂]^(T)=π^((D)) s,  [Eqn. 11]

{tilde over (y)}=Q ^((D)H) y=R ^((D)) {tilde over (s)}+ñ ^((D)),

{tilde over (y)} ₁ ^((D)) =R ₁₁ ^((D)) s ₃ +R ₁₃ ^((D)) s ₁ +R ₁₄ ^((D))s ₂ +ñ ₁ ^((D))

{tilde over (y)} ₂ ^((D)) =R ₁₁ ^((D)) s ₄ +R ₁₄ ^(*(D)) s ₁ −R ₁₃^(*(D)) s ₂ +ñ ₂ ^((D)).

{tilde over (y)} ₃ ^((D)) =R ₃₃ ^((U)) s ₁ +ñ ₃ ^((D))

{tilde over (y)} ₄ ^((D)) =R ₃₃ ^((D)) s ₂ +ñ ₄ ^((D))  [Eqn. 12]

Similar to Equation 8 that decides the LLRs of [s₃, s₄]^(T), the LLRs of[s₁, s₂]^(T) are decided by:

$\begin{matrix}{{\Phi^{(D)}\text{:}\mspace{14mu} {candidate}\mspace{14mu} {vector}\mspace{14mu} {from}\mspace{14mu} {all}\mspace{14mu} {possible}\mspace{14mu} {combinations}\mspace{14mu} {of}\mspace{14mu} s_{1}\mspace{14mu} {and}\mspace{14mu} s_{2}\mspace{14mu} {with}\mspace{14mu} D\; F\mspace{14mu} {detection}}\mspace{79mu} {{{\Phi^{(D)}}\text{:}\mspace{14mu} {the}\mspace{14mu} {cardinality}\mspace{14mu} {of}\mspace{14mu} \Phi^{(D)}},{{i.e.\mspace{11mu} {\Phi^{(D)}}} = {\Omega }^{2}}}\mspace{85mu} {{\overset{\sim}{s}}_{k}\text{:}\mspace{14mu} {element}\mspace{14mu} {of}\mspace{14mu} \Phi^{(D)}}\mspace{79mu} {{{L\; L\; {R\left( b_{i}^{q} \right)}} \approx {\frac{1}{2\sigma^{2}}\begin{pmatrix}{{\min\limits_{{{s_{k} \in \Phi^{(D)}}b_{i}^{q}} = {- 1}}{{\overset{\sim}{y} - {R^{(D)}s_{k}}}}^{2}} -} \\{\min\limits_{{{s_{k} \in \Phi^{(D)}}b_{i}^{q}} = {+ 1}}{{\overset{\sim}{y} - {R^{(D)}s_{k}}}}^{2}}\end{pmatrix}}},\mspace{85mu} {q \in {\left\{ {1,2} \right\}.}}}} & \left\lbrack {{Eqn}.\mspace{14mu} 13} \right\rbrack\end{matrix}$

In summary, the LLRs of each symbol can be determined by:

$\begin{matrix}{{L\; L\; R\mspace{14mu} {{of}\mspace{14mu}\left\lbrack {s_{1},s_{2}} \right\rbrack}^{T}}{{{L\; L\; R\; \left( b_{i}^{q} \right)} \approx {\frac{1}{2\sigma^{2}}\begin{pmatrix}{{\min\limits_{{{s_{k} \in \Phi^{(D)}}b_{i}^{q}} = {- 1}}{{\overset{\sim}{y} - {R^{(D)}{\overset{\sim}{s}}_{k}}}}^{2}} -} \\{\min\limits_{{{s_{k} \in \Phi^{(D)}}b_{i}^{q}} = {+ 1}}{{\overset{\sim}{y} - {R^{(D)}{\overset{\sim}{s}}_{k}}}}^{2}}\end{pmatrix}}},{q \in \left\{ {1,2} \right\}}}{L\; L\; R\mspace{14mu} {{of}\mspace{14mu}\left\lbrack {s_{3},s_{4}} \right\rbrack}^{T}}{{{L\; L\; R\; \left( b_{i}^{q} \right)} \approx {\frac{1}{2\sigma^{2}}\begin{pmatrix}{{\min\limits_{{{s_{k} \in \Phi^{(U)}}b_{i}^{q}} = {- 1}}{{\overset{\sim}{y} - {R^{(U)}s_{k}}}}^{2}} -} \\{\min\limits_{{{s_{k} \in \Phi^{(U)}}b_{i}^{q}} = {+ 1}}{{\overset{\sim}{y} - {R^{(U)}s_{k}}}}^{2}}\end{pmatrix}}},{q \in {\left\{ {3,4} \right\}.}}}} & \left\lbrack {{Eqn}.\mspace{14mu} 14} \right\rbrack\end{matrix}$

For example, to compute the LLRs of [s₁, s₂]^(T) by Equation (14),∥{tilde over (y)}−R^((D)){tilde over (s)}_(k)∥² is first computed forevery possible combination of {tilde over (s)}_(k)=[s₁, s₂]^(T) (4²=16combinations, k=0, 1, . . . , 15 in quadrature phase shift keying(QPSK)). Then, bit information included in s₁ (2 bits for a QPSKsymbol), b₀ ¹ and b₁ ¹ and bit information included in s₂, b₀ ² and b₁ ²are calculated based on 16 values of ∥{tilde over (y)}−R^((D)){tildeover (s)}_(k)∥² (k=0, 1, . . . , 15).

To calculate the LLR of b₀ ¹ to thereby determine whether b₀ ¹ is −1 or1, the minimum ∥{tilde over (y)}−R^((D)){tilde over (s)}_(k)∥² of symbolvectors with b₀ ¹=1 among 16 symbol vectors is subtracted from theminimum ∥{tilde over (y)}−R^((D)){tilde over (s)}_(k)∥² of symbolvectors with b₀ ¹=−1.

As described before, the conventional ML detection scheme requires lΩl⁴candidates to calculate the LLR of each bit. In comparison, the first MLdetection scheme of the present invention needs only lΩl² candidates.When the LLRs of all bits included in one transmitted symbol vector arecalculated, the number of candidates to be compared increases to lΩl⁴×4log₂lΩl in the conventional ML detection scheme, the present inventioncan decrease the number of candidates because candidates are comparednot on a bit basis but on a symbol basis:

1st bit‘0’:I<0

1st bit‘1’:I>0

2nd bit‘0’:Q<0

2nd bit‘1’:Q>0.  [Eqn.15]

In accordance with the present invention, the Euclidean distances ofsymbols from the origin on a constellation are calculated and each bitcan be extracted by applying the Euclidean distances to Equation 15. Inother words, the Euclidean distance of each candidate vector iscalculated, rather than the Euclidean distances of all bits arecalculated and each bit of an intended candidate vector is extractedaccording to Equation 15.

Equation 15 describes how to distinguish eight symbol vectors with b₀¹=−1 from eight symbol vectors with b₀ ¹=1. In other words, if theinteger component of s₁ in {tilde over (s)}_(k) is larger than 0, b₀ ¹=1and if the integer component of s₁ is less than 0, b₀ ¹=−1.

The first ML detection scheme has been described above. Now adescription will be made of the second ML detection scheme.

2. Second ML Detection Scheme

The computation of an optimal LLR of each bit included in [s₁, s₂]^(T)can be modeled to a closest-point search (CPS) problem. By max-logapproximation, the optimal LLR can be computed by Equation 13. For [s₁,s₂], Equation (13) can be expressed as:

$\begin{matrix}{{{L\; L\; {R\left( b_{i}^{q} \right)}} \approx {\frac{1}{2\sigma^{2}}\begin{pmatrix}{\underset{\underset{{part}\mspace{14mu} A}{}}{\min\limits_{{s_{k}b_{i}^{q}} = {- 1}}{{{\overset{\sim}{y}}^{(U)} - {R^{(U)}s_{k}}}}^{2}} -} \\\underset{\underset{{part}\mspace{14mu} B}{}}{\min\limits_{{s_{k}b_{i}^{q}} = {+ 1}}{{{\overset{\sim}{y}}^{(U)} - {R^{(U)}s_{k}}}}^{2}}\end{pmatrix}}}{{q \in \left\{ {1,2} \right\}},{{i\text{:}\mspace{14mu} {the}\mspace{14mu} i} - {{th}\mspace{14mu} {bit}}}}} & \left\lbrack {{Eqn}.\mspace{14mu} 16} \right\rbrack\end{matrix}$

The computation of the optimal LLR amounts to computation of the minimumvalues of part A and part B in Equation 16. Thus,

$\begin{matrix}\begin{matrix}{{{minimum}\mspace{14mu} {of}\mspace{14mu} {part}\mspace{14mu} A\text{:}\mspace{14mu} {\min\limits_{{s_{k}b_{i}^{q}} = {- 1}}{{{\overset{\sim}{y}}^{(U)} - {R^{(U)}s_{k}}}}^{2}}}\;} \\{{minimum}\mspace{14mu} {of}\mspace{14mu} {part}\mspace{14mu} B\text{:}\mspace{14mu} {\min\limits_{{s_{k}b_{i}^{q}} = {+ 1}}{{{{\overset{\sim}{y}}^{(U)} - {R^{(U)}s_{k}}}}^{2}.}}}\end{matrix} & \left\lbrack {{Eqn}.\mspace{14mu} 17} \right\rbrack\end{matrix}$

The minimization problem of Equation 17 is no better than the CPSproblem. The CPS problem requires searching for s_(k) with minimumvalues according to Equation 17. To distinguish s_(k) with minimumvalues from other s_(k), s_(k) with a minimum value for an i^(th) bit isrepresented as Λ_(q,i,k) where q is the index of a transmit antenna, iis the index of a bit, and k is +1 or −1.

$\begin{matrix}{{{In}\mspace{14mu} {summary}},{\Lambda_{q,i,k} = {\arg {\min\limits_{{s_{k}b_{i}^{q}} = j}{{{\overset{\sim}{y}}^{(D)} - {R^{(D)}s_{k}}}}^{2}}}},{{{where}\mspace{14mu} q} \in \left\{ {1,2} \right\}},{k \in \left\{ {{+ 1},{- 1}} \right\}},{{{and}\mspace{14mu} {\min\limits_{{s_{k}b_{i}^{q}} = j}{{{\overset{\sim}{y}}^{(D)} - {R^{(D)}s_{k}}}}^{2}}} = {{{{\overset{\sim}{y}}^{(D)} - {R^{(D)}\Lambda_{q,i,k}}}}^{2}.}}} & \left\lbrack {{Eqn}.\mspace{14mu} 18} \right\rbrack\end{matrix}$

Thus, the optimal LLR is achieved by:

$\begin{matrix}{{{L\; L\; {R\left( b_{i}^{q} \right)}} \approx {\frac{1}{2\sigma^{2}}\begin{pmatrix}{{{{\overset{\sim}{y}}^{(D)} - {R^{(D)}\Lambda_{q,i,{- 1}}}}}^{2} -} \\{{{\overset{\sim}{y}}^{(D)} - {R^{(D)}\Lambda_{q,i,{+ 1}}}}}^{2}\end{pmatrix}}},{q \in {\left\{ {1,2} \right\}.}}} & \left\lbrack {{Eqn}.\mspace{14mu} 19} \right\rbrack\end{matrix}$

The CPS problem of Equation 18 is equivalent to the minimization problemgiven as Equation 20:

$\begin{matrix}\begin{matrix}{\Psi_{q,i,k} = {{{\overset{\sim}{y}}^{(D)} - {R^{(D)}\Lambda_{q,i,k}}}}^{2}} \\{= {\min\limits_{{s_{k}b_{i}^{q}} = k}{{{\overset{\sim}{y}}^{(D)} - {R^{(D)}s_{k}}}}^{2}}} \\{{= {\min\limits_{{s_{k}b_{i}^{q}} = k}{f\left( {s_{1},s_{2},s_{3},s_{4}} \right)}}},}\end{matrix} & \left\lbrack {{Eqn}.\mspace{14mu} 20} \right\rbrack\end{matrix}$

where f(s₁,s₂,s₃,s₄)=∥{tilde over (y)}^((D))−R^((D))s_(k)∥². As statedbefore, it is known from a partially orthogonal channel matrix thats₃,s₄ are dependent on s₁,s₂. Thus, Equation 20 can be simplified to:

$\begin{matrix}{\Psi_{q,i,k} = {\min\limits_{{s_{1} \in \Omega},{{{s_{2} \in \Omega}b_{i}^{q}} = k}}{{f\left( {s_{1},s_{2}} \right)}.}}} & \left\lbrack {{Eqn}.\mspace{14mu} 21} \right\rbrack\end{matrix}$

As a candidate vector of s₃,s₄ with a minimum distance in Φ(U) is ahard-decision ML value, the hard-decision ML solution of [ŝ₁,ŝ₂]^(T) iseasily calculated. According to the present invention, an LLR iscalculated after all as follows. The distance of a symbol is theEuclidean distance of the symbol from the origin on a signalconstellation.

If the hard-decision ML solution ŝ is known, the minimization problem ofEquation 21 is posed as a relaxed minimization problem described by thefollowing Equation:

$\begin{matrix}\begin{matrix}{\Psi_{q,i,k} = {\min\limits_{{s_{1} \in \Omega},{{{s_{2} \in \Omega}b_{i}^{q}} = k}}{s\left( {s_{1},s_{2}} \right)}}} \\{\leq {\min\limits_{{{s_{2} \in \Omega}b_{i}^{q}} = k}{f\left( {{\hat{s}}_{1},s_{2}} \right)}}} \\{{\leq {\min\limits_{{{s_{1} \in \Omega}b_{i}^{q}} = k}{f\left( {s_{1},{\hat{s}}_{2}} \right)}}},}\end{matrix} & \left\lbrack {{Eqn}.\mspace{14mu} 22} \right\rbrack\end{matrix}$

where ŝ_(k) denotes a k^(th) element of the hard-decision ML solution ŝ.Therefore, the complexity of solving the relaxed minimization problemdecreases from O(|Ω|²) to o(2|Ω|). Herein, O(o) represents computationalvolume. As described above, when a solution is detected by minimization,the complexity is considerably reduced in a high-order modulation schemesuch as 16-ary quadrature amplitude modulation (16QAM). [s₃,s₄]^(T) canbe detected using [ŝ₁,s₂]^(T) and [s₁,ŝ₂]^(T), and a new candidatevector set Φ_(n), can be formed. Here, |Φ_(n)|=2|Ω|. Φ_(n) includesinformation about all bits of s₁ and s₂ and to provide more informationfor LLR calculation, Φ=Φ^((U))∪Φ_(n) is computed. Since Φ⊃Φ^((U)) forbits included in [s₃,s₄]^(T), optimal LLRs are provided conventionally.On the other hand, candidate vectors are obtained for bits included in[s₁,s₂]^(T) by the relaxed minimization problem, and thus sub-optimalLLRs are produced. Accordingly, LLRs are computed in the second MLdetection scheme of the present invention by:

$\begin{matrix}{{{L\; L\; {R\left( b_{i}^{q} \right)}} \approx {\frac{1}{2\sigma^{2}}\begin{pmatrix}{{\min\limits_{{{s_{k} \in \Phi}b_{i}^{q}} = {- 1}}{{{\overset{\sim}{y}}^{(U)} - {R^{(U)}s_{k}}}}^{2}} -} \\{\min\limits_{{{s_{k} \in \Phi}b_{i}^{q}} = {+ 1}}{{{\overset{\sim}{y}}^{(U)} - {R^{(U)}s_{k}}}}^{2}}\end{pmatrix}}},} & \left\lbrack {{Eqn}.\mspace{14mu} 23} \right\rbrack\end{matrix}$

where Φ=Φ^((U))∪Φ_(n).

FIG. 2 is a detailed block diagram of a first ML detector according toan exemplary embodiment of the present invention.

Referring to FIG. 2, a symbol detector 201 forms a received signalvector by detecting symbols received during two OFDM symbol intervals. Achannel estimator 203 estimates channels using the received symbols andoutputs the estimated channel information, i.e., an equivalent channelmatrix to a QR decomposer 205.

The QR decomposer 205 QR-decomposes the equivalent channel matrix andprovides the QR decomposition result to a Q^((U)H) multiplier 207 and aQ^((D)H) multiplier 209. The Q^((U)H) multiplier 207 and the Q^((D)H)multiplier 209 multiply the received signal vector by Q^((U)H) andQ^((D)H), respectively.

An (s₃, s₄) symbol generator 211 and an (s₁, s₂) symbol generator 213generate all candidate symbol combinations for s₃ and s₄ and for s₁ ands₂, respectively.

An adder/subtractor 208 eliminates s₃ and s₄ components from a receivedsignal vector {tilde over (y)}₁ ^((U)) and {tilde over (y)}₂ ^((U)). An(s₁, s₂) hard-decider 215 performs hard decision on symbols s₁ and s₂from the received signal vector free of the s₃ and s₄ components.Similarly, an adder/subtractor 210 eliminates s₁ and s₂ components froma received signal vector {tilde over (y)}₁ ^((U)) and {tilde over (y)}₂^((U)). An (s₃, s₄) hard-decider 217 performs hard decision on symbolss₃ and s₄ from the received signal vector free of the s₁ and s₂components.

An (s₃, s₄) LLR calculator 219 forms candidate vectors using thehard-decided symbols s₁ and s₂ and the combinations of s₃ and s₄generated from the (s₃, s₄) symbol generator 211 and calculates the LLRsof bits forming the symbols s₃ and s₄.

Similarly, an (s₁, s₂) LLR calculator 221 forms candidate vectors usingthe hard-decided symbols s₃ and s₄ and the combinations of s₁ and s₂generated from the (s₁, s₂) symbol generator 213 and calculates the LLRsof bits forming the symbols s₁ and s₂.

FIG. 3 is a detailed block diagram of a second ML detector according toanother exemplary embodiment of the present invention.

Referring to FIG. 3, the second ML detector further includes a summer323 and has a modified symbol generator 313 to implement a second MLdetection scheme.

In the second ML detector, the symbol generator 313 generates candidatevectors with minimum distances for s₃ and s₄. The symbol generator 313includes an (ŝ₁,s₂) generator 313 a for generating symbols ŝ₁ and s₂ andan (s₁,ŝ₂) generator 313 b for generating symbols s₁ and ŝ₂. Since s₃and s₄ are dependent on s₁ and s₂ as noted from Equation 20 and Equation21, s₃ and s₄ can be created using s₁ and s₂. The summer 323 calculatesfinal LLRs by combining two candidate vectors.

FIG. 4 is a flowchart illustrating an ML detection operation in thereceiver according to an exemplary embodiment of the present invention.

Referring to FIG. 4, the receiver detects symbols corresponding to areceived signal in step 402 and estimates channels in step 404. Thereceiver permutes an equivalent channel matrix using a predeterminedpermutation matrix in step 406.

The receiver QR-decomposes the permuted equivalent channel matrix instep 408 and branches off into steps 410 and 420.

In step 410, the receiver creates all possible symbol combinations fors₁ and s₂. The receiver then eliminates s₁ and s₂ symbol components fromthe received signal in step 412 and makes a hard decision on s₃ and s₄in step 414. In step 416, the receiver determines the LLRs of bitsforming s₁ and s₂.

In step 420, the receiver creates all possible symbol combinations fors₃ and s₄. The receiver then eliminates s₃ and s₄ symbol components fromthe received signal in step 422 and makes a hard decision on s₁ and s₂in step 424. In step 426, the receiver determines the LLRs of bitsforming s₃ and s₄.

FIG. 5 is a graph comparing the ML detection schemes according to theexemplary embodiments of the present invention with a conventional MLdetection scheme in terms of computational volume.

A simulation was performed under the following conditions.

TABLE 1 Parameters Value Bandwidth 20 MHz Number of subcarriers 64Subcarrier spacing 0.3125 MHz Guard interval 0.8 μsec Symbol interval4.0 μsec Numbers of transmit and 4Tx Ant/2Rx Ant receive antennasModulation scheme QPSK/16QAM Channel coding Convolutional code, R = ½, K= 7, g = [133 171]₈ Channel model Uniformly distributed channels (14paths)

The graph illustrated in FIG. 5 reveals that the conventional MLdetection scheme requires a larger computational volume than the MLdetection schemes of the present invention. The first ML detectionscheme (Proposed ML1) calculates LLRs after calculating the distance ofeach bit, and the second ML detection scheme (Proposed ML2) extracts bitinformation and calculates LLRs after calculating the distance of eachsymbol.

As is apparent from the above description, the present inventionadvantageously reduces the volume of LLR computation by providing thesimplified ML detection schemes.

Although the present disclosure has been described with an exemplaryembodiment, various changes and modifications may be suggested to oneskilled in the art. It is intended that the present disclosure encompasssuch changes and modifications as fall within the scope of the appendedclaims.

1. A method for detecting a signal in a receiver by maximum likelihood(ML) comprising: detecting symbols from a received signal according tothe number of transmit antennas of a transmitter and a modulationscheme; estimating channels using the detected symbols; determining anequivalent channel matrix corresponding to the estimated channels;determining a permuted equivalent channel matrix by multiplying theequivalent channel matrix by a predetermined permutation matrix;performing QR decomposition on the permuted equivalent channel matrix;performing a hard decision on first symbols among the detected symbolsusing symbols obtained from the QR decomposition; and determining thelog likelihood ratios (LLRs) of second symbols other than the firstsymbol among the detected symbols using the hard-decided symbols andcombinations of the first symbols.
 2. The method of claim 1, wherein thepredetermined permutation matrix is: $\Pi^{(U)} = {\begin{bmatrix}1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & 1 & 0 \\0 & 0 & 0 & 1\end{bmatrix}.}$
 3. The method of claim 1, wherein the predeterminedpermutation matrix is: $\Pi^{(D)} = {\begin{bmatrix}0 & 0 & 1 & 0 \\0 & 0 & 0 & 1 \\1 & 0 & 0 & 0 \\0 & 1 & 0 & 0\end{bmatrix}.}$
 4. The method of claim 1, wherein the result fromQR-decomposing the permuted equivalent channel matrix is:$R^{(U)} = {\begin{bmatrix}R_{1,1}^{(U)} & 0 & R_{1,3}^{(U)} & R_{1,4}^{(U)} \\0 & R_{1,1}^{(U)} & {- R_{1,4}^{{(U)}*}} & R_{1,3}^{{(U)}*} \\0 & 0 & R_{3,3}^{(U)} & 0 \\0 & 0 & 0 & R_{3,3}^{(U)}\end{bmatrix}.}$
 5. The method of claim 1, wherein the result fromQR-decomposing the permuted equivalent channel matrix is:$R^{(D)} = {\begin{bmatrix}R_{1,1}^{(D)} & 0 & R_{1,3}^{(D)} & R_{1,4}^{(D)} \\0 & R_{1,1}^{(D)} & {- R_{1,4}^{{(D)}*}} & R_{1,3}^{{(D)}*} \\0 & 0 & R_{3,3}^{(D)} & 0 \\0 & 0 & 0 & R_{3,3}^{(D)}\end{bmatrix}.}$
 6. The method of claim 1, wherein the LLR determinationcomprises: eliminating components corresponding to the second symbolsfrom the received signal to output a received signal free of thecomponents corresponding to the second symbols; performing a harddecision on the first symbols from the received signal free of thecomponents corresponding to the second symbols; and calculating the loglikelihood ratios (LLRs) of the second symbols using the hard-decidedsymbols and candidate symbol combinations of the first symbols.
 7. Themethod of claim 6, further comprising detecting a symbol with a minimumvalue in the second symbols after the hard decision.
 8. An apparatus fordetecting a signal by maximum likelihood (ML) in a receiver, comprising:a symbol detector for detecting symbols from a received signal accordingto the number of transmit antennas of a transmitter and a modulationscheme; a channel estimator for estimating channels and determining anequivalent channel matrix corresponding to the estimated channels; a QRdecomposer for determining a permuted equivalent channel matrix bymultiplying the equivalent channel matrix by a predetermined permutationmatrix and performing QR decomposition on the permuted equivalentchannel matrix; and a log likelihood ratios (LLR) calculator forperforming hard decision on first symbols among the detected symbolsusing the symbols obtained from the QR decomposition and determining thelog likelihood ratios (LLRs) of second symbols other than the firstsymbol among the detected symbols using the hard-decided symbols andcombinations of the first symbols.
 9. The apparatus of claim 8, whereinthe predetermined permutation matrix is: $\Pi^{(U)} = {\begin{bmatrix}1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & 1 & 0 \\0 & 0 & 0 & 1\end{bmatrix}.}$
 10. The apparatus of claim 8, wherein the predeterminedpermutation matrix is: $\Pi^{(D)} = {\begin{bmatrix}0 & 0 & 1 & 0 \\0 & 0 & 0 & 1 \\1 & 0 & 0 & 0 \\0 & 1 & 0 & 0\end{bmatrix}.}$
 11. The apparatus of claim 8, wherein the result fromQR-decomposing the permuted equivalent channel matrix is:$R^{(U)} = {\begin{bmatrix}R_{1,1}^{(U)} & 0 & R_{1,3}^{(U)} & R_{1,4}^{(U)} \\0 & R_{1,1}^{(U)} & {- R_{1,4}^{{(U)}*}} & R_{1,3}^{{(U)}*} \\0 & 0 & R_{3,3}^{(U)} & 0 \\0 & 0 & 0 & R_{3,3}^{(U)}\end{bmatrix}.}$
 12. The apparatus of claim 8, wherein the result fromQR-decomposing the permuted equivalent channel matrix is:$R^{(D)} = {\begin{bmatrix}R_{1,1}^{(D)} & 0 & R_{1,3}^{(D)} & R_{1,4}^{(D)} \\0 & R_{1,1}^{(D)} & {- R_{3,3}^{(D)}} & 0 \\0 & 0 & R_{3,3}^{(D)} & 0 \\0 & 0 & 0 & R_{3,3}^{(D)}\end{bmatrix}.}$
 13. The apparatus of claim 8, further comprising: ahard decider for eliminating components corresponding to the secondsymbols from the received signal to output a received signal free of thecomponents corresponding to the second symbols, and performing a harddecision on the second symbols from the received signal free of thecomponents corresponding to the first symbols.
 14. The apparatus ofclaim 13, wherein the symbol generator detects a symbol with a minimumvalue in the second symbols after the hard decision.